Given three non-overlapping spheres in space with different radii, calculate the volume of the convex hull formed by all points inside the three spheres.
Input
The input consists of three lines, each containing four integers $x_i, y_i, z_i, r_i$ ($1 \leq r_i \leq 100, 0 \leq x_i, y_i, z_i \leq 100$).
Output
Output a single real number representing the answer. Your answer will be considered correct if the absolute or relative error does not exceed $10^{-6}$.
Examples
Input 1
10 0 0 1
0 10 0 2
0 0 10 3Output 1
691.832383333484585819Subtasks
| Test Case ID | Special Properties |
|---|---|
| $1$ | $y_i=z_i=0$ |
| $2 \sim 3$ | $z_i = 0$ |
| $4 \sim 5$ | $x_1 < x_2 < x_3, y_1 < y_2 < y_3, z_1 < z_2 < z_3$ |
| $6 \sim 10$ | No additional constraints |